Lecture Groundwater Hydrology

5/22/2018 Lecture Groundwater Hydrology

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Groundwater Hydrology

Guchie Gulie (Lecturer)Arba Minch University,

Department of Water Resources

and Irrigation Engineering


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Contents

9Groundwater modeling9

8Artificial recharge of groundwater8

7Groundwater quality and its monitoring7

6Pumping test6

5Well hydraulics: steady and unsteady flow, multiplewell system

5

4Fundamentals of groundwater movement4

3Aquifers3

2Occurrence of groundwater2

1Groundwater in hydrologic cycle1

ChapterContentsS.N


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Groundwater in Hydrologic cycle

Water on earth circulates in a spacecalled the hydrosphere, which extendsabout 15km up in to the atmosphereand about 1km down into thelithosphere


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Hydrologic cycle

Inflow Outflow =change in storage


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5Animation of Hydrological processes in an area


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Usually groundwater constitutes part of thehydrologic cycle which lies under the surface

of the ground.

But Connate waters are those which have beenout of the water cycle for at least an appreciable

part of the geological period. They consist

essentially of fossil interstitial water that has

migrated from its original burial location bymeans of various phenomena. Being also

entrapped within particular groundwater

reservoirs, they are typically highly mineralized.

They may have been derived from oceanic orfresh water sources.


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Magmatic waters are those which are

derived from magmas through

hydrothermal phenomena.

Metamorphic waters are those which are orhave been associated with rocks during

their metamorphism.


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Sources of natural recharge to groundwater include:

precipitation,

stream flows, and lakes

Even sea-water can enter under ground along thecoasts where hydraulic gradient shapes downward

in an inland direction.

Other contributions, known as arti ficial recharge, occur from:

excess irrigation,seepage from canals, reservoirs andwater purposely applied to augmentgroundwater.

However, the ultimate source of groundwater

recharge is assumed to be precipitation


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Most natural discharge from groundwateroccurs as flow into surface water bodies, such

as streams, lakes, and oceans, and to thesurface as springs.

Groundwater near the surface may returndirectly to the atmosphere by evaporation fromthe soil surface and by transpiration fromvegetation.Pumpage from wells constitutes major artificialdischarge of groundwater.


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OCCURRENCE OF GROUNDWATER

Describing the occurrence ofgroundwater needs to review where and

how groundwater exists and itssubsurface distribution, both in verticaland aerial extents.


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The possibility of occurrence and movementof groundwater mainly depends upon two

main geological factories of the rock materials:

porosityCoefficient of permeabil ity


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Aquifer properties that affect

groundwater occurrence & movement

Basic hydrogeological parameters

Porosity

Hydraulic conductivity

compressibility


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Derived hydrogeological parameters

Transmissivity of aquifers

Coefficient of storage (storativity)

Specific yield of aquifers


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Porosity and void ratio Porosity refers the portions of soils and

rocks which are not occupied by solidmatter, but possibly by water and air. These

portions are normally called voids,interstices, pores or empty spaces.

Since these empty spaces serve as waterconduits or storages, they are very important

when groundwater problems are concerned.Open spaces are characterized by their sizes,shapes, irregularities and distributions,

which depend on their origin. Porosity maybe classified as primary or secondary.


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The storage available in an aquifer is

related to the void space that it

contains (total porosity). The totalporosity as percentage is expressed

as

( )100t

v

vv=

Porosity


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Where =total porosity

Vv= volume of void spaces in the sample

Vt = total volume of the sample

There is evident that porosity depends upon

the gradation and shape of soil particle


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Porosity depends on:

Sorting of grains (not only on grain size)

Degree of cementing

Degree of fracturing

Primary porosity, and

Secondary porosity

Types of porosity:


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Secondary porosity are those which develop after

the rocks were formed, and are found in all typesof rocks as joints, fractures, faults, solution

openings, etc.

Primary porosity are those which are originated by

the same geological processes which gave rise to

the various geological formations, and are found insedimentary, igneous and metamorphic rocks.


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Porosity

(Primary and secondary)


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Values of porosity


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Void ratio (e):

It is expressed as the ratio (in percentage) of

the volume of the voids to the volume of the

solid matter:e = (Vv / Vs) x 100


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Vertical profile of water distribution


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1.Soil water zone

2. Intermediate vadose water

zone

3.Capillary water zone

a) Vadose zone

b) Phreatic water zone (zone of saturation)


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Capillary zone (capillary fringe)


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Fu

= cosx 2 rFd = r2 h x g x


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= surface tension of water against air

(= 0.073kg/s2

at 200

c)

= contact angle water with tube (=0 for

water and in pure glass, cos 1)r = equivalent radius of tube (cm)


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= density of water (= 1000kg/m3)

g= acceleration due to gravity (=9.8/m/s2

)h = height of capil lary rise (cm)

Fu = Fd


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gr

gr

rh

gxhrrx

cos2

2cos

2cos

2

2

=

=

=


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215.0

,&,

cmrh

getwegofvaluesthengSubstituti

=


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Phreatic water zone

In this zone, groundwater fills all of the interstices.

Hence the porosity provides a direct measure of thewater contained per unit volume of the formation in

that zone. A portion of water can be removed from

the strata of this zone by drainage or pumping well.

The zone below the water table is generally calledphreatic water zone and the water in this zone is

termed as groundwater.


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Properties of formation materias Infiltrability

Coefficient of permeability Hydraulic conductivity

Compressibilty

Transmissivity

Coefficient of storage (Storativity)

Specific yield of aquifers Hydaulic resistance


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Types of Geologic formations (based on

water storing and transmitting capability)

i) Aquifers:

ii) Aquicludes

iii) Aquifuge

iV) Aquitard


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Geologic formations as Aquifers

I. Unconsolidated or loosely consolidated

sand and gravel deposits (Fluvial and

Aeolian deposits). These generally formthe best aquifers


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The fluvial deposits are the materials laiddown by physical processes in river channels

or on flood plains. These materials are also

known as alluvial deposits. Probably 90percent of all developed aquifers in the world

consists unconsolidated rocks, chiefly gravel

and sand, which are of alluvial origin. These

aquifers may be divided into four categories,

based on manner of occurrence, as:

Fluvial Deposits .


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1.Water courses,

2.Abandoned or buried valleys,

3.Plains, and

4. Intermountain valleys


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Materials that are transported and deposited

by wind are known as Aeolian deposits.

Aeolian deposits consist of sand or siltmaterials. Aeolian deposits of sil t are known

as leoss.

Aeolian deposits:


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II. Semi-consolidated and consolidated

conglomerate (the consolidated

equivalent of gravel) and sandstoneformations

Their water yielding capacity depends up onthe degree of cementation. Partially cemented

and fractured sandstones are the best type of

these formations.


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III. Carbonate formations like limestone,

marble, dolomite, etc

Carbonate rocks with primary porosity, such as

old unfractured limestone and dolomite, areusually important in petroleum mining rather

than as the significant sources of groundwater.


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But sometimes openings in limestone may rangefrom microscopic original pores to secondary large

solution caverns forming subterranean channels

sufficiently large enough to carry the entire flow of

a stream. The term lost river has been applied to astream that disappears completely underground in

a limestone terrain. Large springs are frequently

found in limestone areas.


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IV.Volcanic Rock

They are generally not porous, but whenthey are poured on the surface of the

earth by volcanic eruption and jointed

and fractured due cooling of the volcaniclava, they form satisfactory formations

that can hold and bear groundwater


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Volcanic rock can form highly permeable

aquifers; basalt flows, in particular, often

display such characteristics. The types of

openings contributing to the permeability

of basaltic aquifers include, in order ofimportance:


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1.Interstitial spaces in clinker lava at the

tops of flows,

2.Cavities between adjacent lava beds,

3.Shrinkage cracks,

4.Lava tubes,

5.Gas vesicles,


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6.Fissures resulting from faulting and

cracking after rocks have cooled, and

7.Holes left by the burning of trees

overwhelmed by lava.


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Types of Aquifers (Aquifer conditions)

1.Unconfined Aquifers

Perched Water1.Semi-confined /leaky aquifers

2.Confined aquifers

aquifers


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aquifers


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Artisian aquifers (flowing wells)


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Artisian aquifers (flowing wells)


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o

1

o

1


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Fundamentals of groundwater flow

p

Elevation, z = z

Pressure p = p

Velocity V = V

Density p = p

Volume of unit mass U = 1/p

Arbitrary standard state

Elevation z = o,Pressure p = po,Velocity V = o,

Density o, and

Volume of unit mass = 1/o

Energy contained in groundwater


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1) Potential Energy, W1:

W1 = mgz

2) Kinetic Energy, W2

2

2

2

mVW =

3) The work required to be done on the fluid in

raising the fluid pressure from p = po to p, w3

=p

po

VdpW3 == P

P

P

Po o

dp

mdpm

V

m


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Total Energy, WT:

WT = W1 + W2 + W3

+=mgzWT +2

2

mV

p

po

dpm

++= P

PT

o

dpmmVmgzW2

2


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The total water potential (total mechanical

energy per unit mass), , is given by:

m

WT=

oppVgz ++=2

2

The total hydraulic head (total mechanicalenergy per unit weight), H, is given by:

g

p

g

V

ZgH

++== 2

2


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Darcys Law:

Who was Henry Darcy?

Henry Darcy was born in Dijon,

in the Southern part of France,in 1803.

Darcy cont


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He enrolled at the Ecole Polytechnique in Paris

in 1821, and then continued in 1823 to study at

the Ecole des Ponts in Chaussees.

His studies led him to a position with the

Dept. of Bridges & Roads

One of his main early projects was the water

supply system (pressure pipes) for the city of

Dijon, bringing water by a covered aqueduct

from the Roster Spring, some 12.7 km from the

city, to a reservoir. He was also involved in

many other projects, as well as in city politics

Darcy cont.

Darcy cont


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During the period, he modified the Prony equation

for calculating the head loss in pipes, due to

friction. Later, this equation was further modified

by Julius Weisbach to become the well knownDarcy-Weisbach equation for head losses in

pipes.

Darcy cont.

His lifelong goal was to convert the water supply

system of the city of Dijon, which was using highly

polluted water from shallow wells and streams to a

centralized water distribution system that hedesigned.

Darcy cont


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In 1848 he became the Chief Engineer for the

Department of Cote-d`Or (around Dijon). However,

due to political pressure, he had to leave to become

the Chief Director for Water and Pavements in Paris.

But due to poor health, he resigned and returned to

Dijon in 1855, where he continued his research.

During 1855-1856, he devoted his research to study

the flow of water and the resulting head loss in sand

columns. This research led to what we refer to asDARCYs LAW. The motivation for this research:

filtration of the water for the fountains of the city of

Dijon.

Darcy cont.

Th d l i t l t

Darcy cont.


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Original modified

The sand column experimental setup:

Darcy cont


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Flow rate, Q, is proportional to head difference, cross-

sectional area and inversely proportional to the length

of the sand column. That is:

Darcy cont.

AL

h

KQ

AL

hQ

=

in which K is a coefficient of proportionality that

depends on the permeability of the sand, h is head

difference,A is cross-sectional area and L is lengthof sand column.

To visualize the flow phenomena in porous medium


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like soil, lets consider the flow between two parallelplates, one at rest and the other moving with constant

velocity (u):


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dy

dus

dy

du

s =

Where the proportionality constant, , is the dynamicviscosity of the fluid.


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s

x

y

PoP1 L

2R

U(y)

R y

Now, lets consider a fluid flow through a straightcylindrical tube of diameter 2R, laid horizontally:

Consider the coaxial fluid cylinder of length L and

radius y


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The pressure force acting on face-2

Fp1= P1y2The pressure force acting on face-1

Fpo=Poy2

The frictional resistance due to shear

stress, s, is:

F = 2 y Ls


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Fp1-Fpo= P1y2 - Poy2

=Py2

For flow of constant velocity, force of frictional

resistance due to shear stress is equal to the force

due to pressures, p1 and po. i.e:

p y2 = 2 y Ls

py = 2 Ls

L

py

s 2

=

=2

y

L

p


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But we know that:

=2

y

L

p

dy

du

2

y

L

p

dy

du

=

dy

dus =

( )224

)( yRL

pyU

=


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LpRu4

2

max =

The discharge can now be evaluated as thevolume of a paraboloid of revolution as:

Q = (base area x height)

Q =

22

421 R

L

pR

=

L

pRQ

8

4 = Poiseuilles equation

R2 umax


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If we assume that the soil column is composed of n number

of interconnected equal tubes, the total discharge QT can be

expressed as:

QT=nQ

L

pRnQT

8

4 =

ARnBut e =2

porosityeffectivewheree=

columnsoilofareationcrosstotalA sec


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columnsoilofareationcrosstotalA sec=

L

pARQ eT

8

2 =

From Darcys law,

AL

hKQ

T

=

Equating the two equations of Q, we get :

L

pReAL

hK A 8

2 =

h

pR

eK

=

8

2

8

2 gR

e=

gk=


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Thus the parameter k depends on the porosity of themedium, the pore-size distribution of the medium, the

shape, orientation and arrangement of the individual

grains of the medium.

That is, k depends on only the characteristics of the

porous medium and called coefficient of

permeability or just permeability. The term intrinsic

permeability is also used for k

But hydraulic conductivity, K, depends on both the

characteristic of the porous medium and thecharacteristic of the flowing fluid.


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Validity of Darcys Law

It is valid as long as the Re, that indicates the

magnitude of the inertial forces relative to theviscous drag, value does not exceed about 1 (but

sometimes as high as 10).

Darcys equation can be applied with in a certain

limit. It is valid only if the flow is laminar.


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The kinematics viscosity and permeability are given as:

= 1.12 cm2/sec and

k = 7.5 darcys (1 Darcy = 9.87x 10-9cm2).

Determine the value of the hydraulic conductivity of theaquifer .

Example


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77y VzVy

x

z

Vx

3-D Flow in homogeneous and isotropic formation:

Consider a volume element of porous medium in the shape ofcubic parallelepiped inside a space defined by a set of

rectangular coordinates x, y, z, as shown in the figure blow

dzzvV zz

+

dyy

vV

y

y

+

dxx

vV xx

+


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Volume of water inflowing in unit time, dt, in x, y, z

directions:

Vx dy dz dt + Vy dz dx dt+ Vz dx dy dt

Volume of water out flowing in unit time, dt, in x, y, z

directions:

dtdydxdxz

vVzdtdxdzdy

y

vVdydtdzdx

x

VV z

y

yx

x

++

++

+=

=


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Volume

inflowing in

unit time dt

Volume out

flowing in unit

time dt

Change

in storage

moisture

storageinchangez

v

y

v

x

v zyx =++

From Darcys Law:

zHKV

yHKV

xHKV zzyyxx

=== ,,

For steady flow:


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y

02

2

2

2

2

2

=

+

+

zH

Ky

H

Kx

H

K zyx

0=

+

+

z

HK

zy

HK

yx

HK

x zyx

Horizontal f low through layered Layered


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Horizontal f low through layered Layered

formations

qx3

h1 h2

qx2

qx1K1

K2

K3


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IDKqx 111 =

IDKqx 222 =

IDKqx 333 =

Flow through each layer may be expressed as:

IDKDKDKqqqq xxxx )( 332211321 ++=++=

=

=3

1i

iiDKI

For homogeneous system this would be


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g y

expressed as:

qx = Kx I(D1+D2+D3)

Eliminating qx from both equations, we get an

expression for equivalent horizontal hydraulic

conductivity for layered formations as:

=

==3

1

3

1

i

i

i

ii

x

D

DK

K


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Vertical flow through layered soils


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21

1

1

1

211 hh

K

DVor

D

hhKV zz =

=

32

2

2

2

32

2 hhK

DVor

D

hhKV zz ==

43

3

3

3

433 hh

KDVor

DhhKV zz ==

If we add up, we get

433221

3

3

2

2

1

1 hhhhhhK

D

K

D

K

DVz ++=

++

41 hh =

For a homogeneous system,


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41

321 hhK

DDDV

z

z =

++

Eliminating (h1-h4), we get an expression for

equivalent vertical hydraulic conductivity of

layered formations as:

3

3

2

2

1

1

321

K

D

K

D

K

D

DDDKz

++

++=

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Lecture Groundwater Hydrology

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